An idealized continuum model of electrokinetic transport is developed to analyze the contributions of solute and barrier charge to microvascular permeability. The glycocalyx fiber-matrix-filled interendothelial cleft of the transcapillary exchange barrier is modelled with parallel plates representing endothelial cell surfaces and a bridging regular array of identical cylinders representing glycocalyx fibers. To calculate the electrostatic potential within the confined fiber-matrix, the linear Poisson-Boltzmann equation is solved for a single bounded post and a regular array of bounded posts using several analytical methods (separation of variables, Green's functions and linear superposition and unit cell approximations) and numerical methods (direct formulation of a boundary element method and boundary collocation method). The potential decays monotonically with distance from the surfaces vanishing between four and five Debye lengths. For values typical of plasma ultrafiltrate in a glycocalyx filled interendothelial cleft, namely a Debye length of 8 A , plate separation of 120 A, post radius of 6 A and surface potential of 60 mV, the potential remains nonzero for porosity values less than 97%. Thus, throughout the confined matrix region of this idealized model, there is enhanced anionic and diminished cationic convective transport compared to neutral molecules. The effect is more pronounced for larger molecules whose double layers extend into double layer regions close to the post or plates where the potential magnitude is greatest. This result agrees with published experimental observations of transport of charged molecules.